Answer: A reflection about the y-axis and a clockwise rotation of 90° around the origin.
another example is:
A counterclockwise rotation of 90° around the origin, and then a reflection about the y-axis.
Step-by-step explanation:
Let's do this for a single point because it is essentially the same.
Let's use the point (3, -2)
First, we have a reflection across the x-axis, this only changes the sign of the y-component.
Then the new point will be: (3, -(-2)) = (3, 2)
Notice that this point is on the first quadrant.
Now we do a 90° counterclockwise rotation.
Then we move to the second quadrant, and we change the order of the components in the point (and because we are in the second quadrant, the x-component is negative and the y-component is positive)
Then the new point is (-2, 3)
Now, another transformation that is equivalent to this one is to do first a reflection about the y-axis, so we only change the sign of the y-component
Then the new point is (-3, -2)
And now we are in the third quadrant.
and then we do a rotation of 90° clockwise, which moves our point to the second quadrant, changes the order of the components and leaves the y-component positive and the x-component negative, then the new point is:
(-2, 3)
Same as before.
(notice that we used the same transformations, but applied to different line and direction of rotation)
Another example is if we first start with a counterclockwise rotation of 90° around the origin, the original point (3, -2) is on the fourth quadrant, so this rotation leaves our point in the first quadrant, so we change the order of the components and both of them will have a positive sign.
The new point is: (2, 3)
Now let's do a reflection about the y-axis, which changes the sign of the x-component.
Then the final point is (-2, 3), same as before.
And there are a lot of other transformations that will be equivalent to this ones, these are just two examples.
